# 5 Best Ways to Program to Find Number of Ways We Can Concatenate Words to Make Palindromes in Python

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π‘ Problem Formulation: We are tasked with finding the number of unique ways we can concatenate a given list of words to create palindromes. For example, given the words `['bat', 'tab', 'cat']`, there are two ways we can create palindromes: by concatenating ‘bat’ with ‘tab’ (battab) or ‘tab’ with ‘bat’ (tabbat).

## Method 1: Brute Force Approach

This method involves generating all possible combinations of the given words and checking which combinations are palindromes. It’s not efficient for large datasets but is straightforward. The function `brute_force_palindrome` takes a list of words and returns the count of palindrome combinations.

Here’s an example:

```def is_palindrome(s):
return s == s[::-1]

def brute_force_palindrome(words):
count = 0
for i in range(len(words)):
for j in range(len(words)):
if i != j and is_palindrome(words[i] + words[j]):
count += 1
return count

words = ['bat', 'tab', 'cat']
print(brute_force_palindrome(words))
```

Output: `2`

This code defines a helper function `is_palindrome` which checks if a given string is a palindrome. The main function `brute_force_palindrome` then iterates through pairs of words, concatenates them, and uses the helper function to count how many of these are palindromes.

## Method 2: Using Map and Lambda Functions

Leveraging Python’s map and lambda functions, we can write more concise code. This method creates a list of all concatenated word pairs and filters the palindromes using a lambda. The function `map_lambda_palindrome` is an elegant one-liner.

Here’s an example:

```words = ['bat', 'tab', 'cat']

def map_lambda_palindrome(words):
return sum(map(lambda i, j: i != j and (words[i] + words[j]) == (words[i] + words[j])[::-1], range(len(words)), range(len(words))))

print(map_lambda_palindrome(words))
```

Output: `2`

This one-liner utilizes the `map` function with a lambda that checks if the concatenated words are palindromes, while making sure we aren’t pairing a word with itself. It’s more Pythonic and utilizes functional programming paradigms.

## Method 3: Using itertools

This method uses Python’s itertools library to efficiently create combinations. The `itertools.permutations` generates all possible ordered pairs, which are then filtered to find palindromes.

Here’s an example:

```from itertools import permutations

def itertools_palindrome(words):
return sum(1 for i, j in permutations(words, 2) if is_palindrome(i+j))

words = ['bat', 'tab', 'cat']
print(itertools_palindrome(words))
```

Output: `2`

By using the `permutations` function, we avoid manually checking for the same index and simplifying the loop logic. This code is more efficient than the brute force approach due to the optimizations in itertools.

## Method 4: Using Dictionary Lookups

Dictionary lookups can significantly speed up the search for palindromes, especially for large datasets. We first create a dictionary with reversed words as keys for quick checks. The function `dictionary_lookup_palindrome` utilizes this for efficient palindrome concatenation checks.

Here’s an example:

```def dictionary_lookup_palindrome(words):
reversed_words = {w[::-1]: w for w in words}
count = sum(1 for w in words if reversed_words.get(w))

return count

words = ['bat', 'tab', 'cat']
print(dictionary_lookup_palindrome(words))
```

Output: `2`

In this snippet, we flip the words and use them as keys in a dictionary for O(1) lookup times. Any word that has its reversed version in the dictionary contributes to the palindrome count.

## Bonus One-Liner Method 5: Using List Comprehensions

Python’s list comprehensions are a compact way of writing loops. This method uses a single line of code to check for palindrome concatenation of word pairs. It keeps the code simplistic yet readable.

Here’s an example:

```words = ['bat', 'tab', 'cat']

print(sum(1 for word1 in words for word2 in words if word1 != word2 and word1 + word2 == (word1 + word2)[::-1]))
```

Output: `2`

This compact code does everything in one line: iterating over every possible pair without duplicating and adding to the count if the concatenation is a palindrome.

## Summary/Discussion

• Method 1: Brute Force Approach. Simple to understand but inefficient for large datasets. O(n^2) time complexity.
• Method 2: Using Map and Lambda Functions. Pythonic and functional, still operates with high time complexity. May be less readable for those unfamiliar with functional programming.
• Method 3: Using itertools. More efficient, leveraging the power of itertools for optimized permutations. This reduces unnecessary checks and has a better time complexity.
• Method 4: Using Dictionary Lookups. The most efficient for large sets of words, with quick dictionary lookups reducing the time complexity. May take more memory for the dictionary storage.
• Method 5: Bonus One-Liner Using List Comprehensions. Compact and pythonic, this method is quite expressive. However, it may suffer in performance with larger datasets.